High-Q Substrate-Integrated-Waveguide Resonator with Degenerate Band Edge

The novel concept of degenerate band edge (DBE) has been recently proposed by Figotin et al., in the framework of their study of slow wave propagation in photonic crystals [1]. The degenerate band edge is a special dispersion condition near the edge of the Brillouin zone ( kd=π/p, p is the spatial period) where four degenerate Bloch modes coalesce at a same frequency fd (two propagating modes and two evanescent modes). The dispersion relation is locally described by a quartic curve \begin{equation*} f-f_{d}=-\alpha(k-k_{d})^{4} \tag{1} \end{equation*} where fd is the DBE frequency and α is a positive constant that depends on the parameters of the structure.